> On 3 Feb., 09:26, William Hughes <wpihug...@gmail.com> wrote:> > On Feb 3, 8:51 am, WM <mueck...@rz.fh-augsburg.de> wrote:> > >> > > In fact we can say that in a suitable list "every" initial segment of> > > s is contained in some line, since there is no s(n) = (s1, s2, ...,> > > sn) missing. But there is no sensible way of saying "all" initial> > > segment.> >> > We can say "every line has the property that it> > does not contain every initial segment of segment of s"> > There is no need to use the concept "all".> > Yes, and this is the only sensible way to treat infinity. But "every> initial segment" has, inadvertently and only noticed by sharp minds> like those of Brouwer and Weyl, changed into "all initial segments" as> you can see from the question concerning the path of 1/3 in a Binary> Tree that contains only every initial segment of the path of 1/3.

If it is actually a path in a CIBT, meaning that it has an actual inifinity of nodes, then it contains not only every but also all finite initial segments of the binary form of 1/3> > Set theory exists only because of the continued switching between> these two meanings. If I ask for a level omega distinguishing between> "every finite path" and the "actually infinite path", I am railed at> (with full right - a level omega is nonsense). But by sending terms of> a sequence only, information about an infinite sequence has never been> transferred.

If one gives a general form for those terms, one defines ALL of them

In binary, 1/3 is 0.(01), where (01) indicates the infinite string of 01 repeating forever.

And every of actually infinitely many proper fractions has has some finitely expressible binary expression.--